Rotational Motion (1) Kinematics Everything’s analogous to linear kinematics Define angular properties properly and derive the equations of motion by analogy Motion on a Wheel Computer Hard Drive A computer hard drive typically rotates at 5400 rev/minute Find the: • Angular Velocity in rad/sec • Linear Velocity on the rim (R=3.0cm) • Linear Acceleration It takes 3.6 sec to go from rest to 5400 rev/min, with constant angular acceleration. • What is the angular acceleration? Computer Hard Drive Numbers worked out: Examples Consider two points b on a rotating wheel. One on the inside (P) R 1 and the other at the R 2 end (b): • Which has greater an gular velocity? • Which has greater lin ear velocity? Rotation and Translation Rolling without Slipping • In reality, car tires both rotate and translate • They are a good example of something which rolls (translates, moves forward, rotates) without slipping • Is there friction? What kind? Derivation • The trick is to pick your re ference frame correctly! • Think of the wheel as sitting st ill and the ground moving past it with speed V. Velocity of ground (in bike frame) = -ωR => Velocity of bike (in ground frame) = ωR